# Math Help - arithmetic series

1. ## arithmetic series

1. Find S20 for each arithmetic series listed below. A) 70 + 66 + 62 + 58 ...
B) 3 + 9 + 15 + 21...
C) 9 + 16 + 23 ...
D) 3 + 2.5 + 2 + 1.5 ...

Determine S20 for the arithmetic series with properties listed below. A) a = 2x and d = 5x ,
B) t14= 46, and t19= 100

2. Originally Posted by euclid2
1. Find S20 for each arithmetic series listed below. A) 70 + 66 + 62 + 58 ...
B) 3 + 9 + 15 + 21...
C) 9 + 16 + 23 ...
D) 3 + 2.5 + 2 + 1.5 ...

Determine S20 for the arithmetic series with properties listed below. A) a = 2x and d = 5x ,
B) t14= 46, and t19= 100
recall the definition of an arithmetic series. these problems are pretty standard once you have that.

an arithmetic series is one in which the terms are given by the formula

$a_n = a_1 + (n - 1)d$

where $a_n$ is the $n$th term, $a_1$ is the first term, $d = a_2 - a_1 = a_3 - a_2 = ....$ is the common difference, and $n \ge 1$ is an integer

the sum of the first $n$ terms, denoted by $S_n$ is given by

$S_n = \frac {n(a_1 + a_n)}2 = \frac {n[2a_1 + (n - 1)d]}2$

thus, to find $S_{20}$ we use

$S_{20} = \frac {20(2a_1 + 19d)}2$

you should be able to determine $a_1$ and $d$ on your own for these problems